the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

In turbulence-theory, the equations for the dynamics of statistical quantities usually form an infinite system. The coupled momentum equations are the best known example. Such relations can also be derived for the n-point-distribution functions which describe the stochastic state of a tur­ bulent medium at every instant. This will be shown for the case of Vlasov turbulence. In order to obtatin ...

Lattice systems arise in many applications, for example, in chemical reaction theory, image processing, pattern recognition, material science, biology, electrical engineering, laser systems, and so forth. A lattice dynamical system LDS is an infinite system of ordinary differential equations lattice ODEs or of difference equations. In some cases, they arise from spatial discretizations of parti...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

We consider mixed problems for infinite systems of first order partial functional differential equations. Infinite number of deviating functions is permitted, and the delay of an argument may depend also on spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existenc...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

where H is the Hamiltonian (”energy”) and {. , .} is a Poisson bracket on an infinite dimensional phase space, called Poisson manifold. Unlike finite dimensional Hamiltonian systems, which are ordinary differential evolution equations on finite dimensional phase spaces, for which general existence and uniqueness theorems for solutions exist, this is not the case for PDEs. There are no general e...